Simply, is the third world war a possiblity?
Yes, son, it is. So is an asteroid on a collison course for the planet. We need to continue to improve our watchfulness for both. For the next 20 years or so, I'd say the probabilities are about equal, but both are such catastrophic events that they need to be reasonably provisioned against. So study history, and REAL science, and try to pay attention world events and economics and to what motivates people beyond the reach of U.S. cable TV. Try to choose leaders grounded in reality, with a demonstrated knowledge of the world and its peoples.
Theoretically, if one country luanches (sp?) a nuke, will the world be destroyed by the splitting of atoms?
In my mind, it's more of a fantasy, even though I know that it is very possible. Would it really only take one terrorist group, or country, to launch a nuke and start it?
In my mind, highly, highly unlikely. The major nuclear powers leadership are pretty sophisicated about the risks of high intensity war, and the differences between national actions and rougue actions. Even the destruction of a major city, even a major power capital by a single nuclear event would be treated as an incident, not a war trigger, unless it was clearly conducted by a major power. Now there would be a highly emotional period of blaming, and an absolute requirement for hunt down and reprisal that would brook little interference or obstruction. In that period, attempts to shelter apparently guilty parties, or or deny reprisal, COULD lead to percieved threats to national sovereignty and to legitimate rights-of-nations, and escalate into a nation level conflict. But even then, in this age of instant communications and 4-hour trans-oceanic diplomatic flights, a serious nation level confrontation would be more likely to result in something like a renewed Cold War than a hot WWIII. With some pretty serious regional conflicts around the edges.
I wonder who would start the war? My bets are on the USA since, in 10 years our economy will completly collapse and we will become a third world country, probably dominated by cristain society, and we already have an INSANE, STUPID, president as it is, + we also have a stash of nukes somewhere.
If you want to contribute to avoiding major war in your time, you should start by trying to be a realistic as possible about the prospects and leadership of your own nation.
a) The US economy is not going to collapse in 10 years. We may not be the monolithic engine of the world economy that we have been in recent decades, and we may have severe competition with other world regions for petrochemical energy in particular, but we will still be, at the very least, one of the 2 largest and strongest national economies on Earth. Now, it is likely that we will pass through a recession in the next 10 years, but just like every recession since the Great Depression, it will be part of a rolling global recession, and we'll recover from it. Part of the nature of recessionary periods is that the short term bad effects (sometimes unfortunately felt very strongly by certain groups of people) tend to set up the conditions for economic recovery and expansion (industries invest internally, reduce workforce, become more efficient, financial institutions build up reserves, managements change, etc).
BTW, it is a pretty well known sociological effect that younger people tend to see economic slowdowns as much worse than their real impact on the long term economy. Its believed to be just because they haven't experienced and coped with the
normal variability of the economy; basically if you are 20 years old right now, you can't help but think of "good times" as "normal". By the time a person is 45, they have seen the economy go up and down 3 times as adults, and "the waves don't look as big".

"...probably dominated by cristain (sic) society...". Got news for you; the US has been dominated by Christian society for 231+ years. And I'm not being facietious. Christian, or in some views Judeo-Christian (Protestant), values, virtues, and failings are thouroughly integrated into all our institutions...including the ones that honor the rights of individuals to choose their way of thought. Over the last 25 years there has been a very vocal political activist surge by fundamentalist Christian segements who thought that their particular beliefs were being underrepresented in the national governance process, but it is hardly the 1st time. And in general that particular factional surge is fading, not out of existance, but becoming more of a bold thread in the cultural fabric rather than a dominant color. Hey, it happened to the free love, hippy, liberalism of the 60's, 70's, too. Not sure, but planet-care and environmentalism may be the next wave.
c) C',mon. I didn't vote for the guy, but the current president is neither insane nor stupid. On the second point first, he was smart enough to get himself elected president, wasn't he (and I WON'T get into whether the unique 1st electoral situation was "right", because it was constitutionally "correct" and practical, and it was a game that only smart people could play). The conduct of the early Afghanistan Initiative was brilliant; it will probably be studied by strategic scholars for centuries, and the president gets to take credit, he had the con. On the subject of insanity, while he is very fixed to his view of the world, and how the US should act within it, it is not an insane position to believe that it his mission in his presidency, under its circumstances, to present a face of stern strength to the world to the very end. We can argue about whether it is the most effective stance, and about whether the the outcomes of major actions were judged well (hell, I'll argue about a lot of them) but even bad misjudgements are not insanity (Remember, in the beginning 70% of Americans were IN FAVOR of the policy they are most against right now.)
A last point on the subject of the current leadership. By the very nature of your question, you should be thinking more about what the NEXT shift coming into the US corridors of power will be inclined to risk and do, and choosing accordingly. I don't see anyone with a likely chance at the US top job in the next round that I fear would start a rash conflict or toss nukes lightly.
d) Yes, we have a "stash" of nukes. (Actually, a very carefully managed nuclear force structure.) The most likely time for any of them to be rashly used was in 2003, against a numerically superior force with a demonstrated willingness to employ WMD themselves. Didn't happen. Not even a little tiny one when we were trying to nail Saddam. The US is not going to start a throwing nukes for anything less than a major WMD assault upon us. We invented the damn things, we're the only ones who have ever used them, and we are the ones who cleaned up after; the folks who control the US nuke force know better than anyone else (except a few physicists and climatologists) just how much they can ruin a pretty good world.
So, will there be a WWIII? Probably, sometime, - history is a long time - when the right power factions develop and develop uncompromisable positions.
Will it be in the next 10 years? I hardly think so - see the conditions above.
Will it be in the next 20 years? See last answer.
Will there be conflicts involving US national forces over the next 2 decades (current involvments taken as givens)? Almost certainly. We have a lot of interests around the world to provide triggers. Plus we have the most finely honed, flexible military that a modern nation has ever had; its hard to not use your best tools. We're also the big dog for now, and usually leashed; foolish boys will want to poke sticks and step on the grass.
drrider